Reaction–diffusion equations in space–time periodic media

Grégoire Nadin

doi:10.1016/j.crma.2007.10.004

Partial Differential Equations

Reaction–diffusion equations in space–time periodic media
[Équations de réaction–diffusion en milieu périodique en temps et en espace]

Présenté par : Paul Malliavin

Grégoire Nadin ¹

¹ Département de mathématiques et applications, École normale supérieure, 45, rue d'Ulm, Paris 75005, France

Comptes Rendus. Mathématique, Volume 345 (2007) no. 9, pp. 489-493.

Résumé
Abstract

Cette Note traite des équations de réaction–diffusion en milieu périodique à la fois en temps et en espace. Nous établissons des conditions d'existence, d'unicité et de convergence en temps grand pour les solutions de telles équations. Ces conditions sont établies en fonctions de deux valeurs propres principales généralisées associées à une équation linéarisée. Nous établissons plusieurs propriétés de ces deux quantités.

This Note deals with reaction–diffusion in space–time periodic media. We state some conditions for the existence, uniqueness and large-time behavior of the solutions of such equations. These conditions are related to the two generalized principal eigenvalues associated with a linearized equation and we state some properties of these quantities.

Reçu le : 2007-06-06
Accepté le : 2007-09-28
Publié le : 2007-10-31

DOI : 10.1016/j.crma.2007.10.004

Affiliations des auteurs :

Grégoire Nadin ¹

¹ Département de mathématiques et applications, École normale supérieure, 45, rue d'Ulm, Paris 75005, France

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     title = {Reaction{\textendash}diffusion equations in space{\textendash}time periodic media},
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Grégoire Nadin. Reaction–diffusion equations in space–time periodic media. Comptes Rendus. Mathématique, Volume 345 (2007) no. 9, pp. 489-493. doi : 10.1016/j.crma.2007.10.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.004/

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Grégoire Nadin Reaction-diffusion equations in space-time periodic media, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 345 (2007) no. 9, pp. 489-493 | DOI:10.1016/j.crma.2007.10.004 | Zbl:1128.35053

Cité par 7 documents. Sources : Crossref, zbMATH

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